Response Theory via Generative Score Modeling

• URL: http://arxiv.org/abs/2402.01029v3
• Date: Fri, 08 Nov 2024 15:59:46 GMT
• Title: Response Theory via Generative Score Modeling
• Authors: Ludovico Theo Giorgini, Katherine Deck, Tobias Bischoff, Andre Souza,
• Abstract summary: We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT) The methodology enables accurate estimation of system responses, including those with non-Gaussian statistics.
• Score: 0.0
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• Abstract: We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT). The methodology enables accurate estimation of system responses, including those with non-Gaussian statistics. We numerically validate our approach using time-series data from three different stochastic partial differential equations of increasing complexity: an Ornstein-Uhlenbeck process with spatially correlated noise, a modified stochastic Allen-Cahn equation, and the 2D Navier-Stokes equations. We demonstrate the improved accuracy of the methodology over conventional methods and discuss its potential as a versatile tool for predicting the statistical behavior of complex dynamical systems.

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